Air compressors are used to fill gas cylinders, fill tires, power pneumatic tools, blow out debris, perform airbrush painting, and to supply air to submerged divers. Of course they are used in various industrial processes as well.
When used in pneumatic tools, they can provide much more power than traditional electric tools. You see air compressors in nail guns, drills, sanders, polisher, pneumatic hammers, impact wrench, speed saw, and large shearing machines.
Smaller portable air compressor are suitable for home use. Smaller ones can run at 2 to 5 CFM at 70 to 90 PSI. Larger ones run at 10 or more CFM and 100 to 120 PSI. Look for the one with the right power for the job.
An air compressor pressurizes and compresses air which can then be released in quick bursts as needed. It uses an either an electric or gasoline engine to compress the air. Electric ones are best for enclosed spaces and can be plugged in where ever there is an electrical outlet. Gas powered ones are suitable in areas where electricity is not readily available. For example, speed saws used in forestry.
For commercial use, look for air compressors that are classified as "industrial grade". That simply means more horsepower, more CFM, more PSI, and longer run times. Most of these are designed to be stationary with ASME certified air tanks that can hold up to 120 gallons of compressed air. ASME stands for American Society of Mechanical Engineers.
There are two main types of air compressors: positive-displacement or negative displacement types. Most compressors are positive-displacement types which includes piston-type compressors, rotary screw compressors, and vane blade compressors. Examples of negative-displacement types are the centrifugal compressors which are more common in larger applications.